The Gleason-Kahane-Zelazko theorem and function algebras
Vesentini, Edoardo
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 16 (2005), p. 87-108 / Harvested from Biblioteca Digitale Italiana di Matematica
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A theorem due to A. Gleason, J.-P. Kahane and W. Zelazko characterizes continuous characters within the space of all continuous linear forms of a locally multiplicatively convex, sequentially complete algebra. The present paper applies these results to investigate linear isometries of Banach algebras (with particular attention to normal uniform algebras) and of some locally multiplicatively convex algebras. The locally multiplicatively convex algebra of all holomorphic functions on a domain, will be investigated at the end of the paper.

Un teorema dovuto a A. Gleason, J.-P. Kahane e W. Zelazko determina i caratteri continui nello spazio di tutte le forme lineari continue di un'algebra moltiplicativamente localmente convessa e sequenzialmente completa. Nel presente lavoro si applicano questi risultati allo studio delle isometrie lineari di algebre di Banach (con particolare attenzione alle algebre normali uniformi) e di algebre localmente moltiplicativamente convesse. Si studia infine l'algebra localmente moltiplicativamente convessa delle funzioni olomorfe su un dominio.

Publié le : 2005-06-01
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     author = {Edoardo Vesentini},
     title = {The Gleason-Kahane-Zelazko theorem and function algebras},
     journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
     volume = {16},
     year = {2005},
     pages = {87-108},
     zbl = {1225.46040},
     mrnumber = {2227745},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RLIN_2005_9_16_2_87_0}
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Vesentini, Edoardo. The Gleason-Kahane-Zelazko theorem and function algebras. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 16 (2005) pp. 87-108. http://gdmltest.u-ga.fr/item/RLIN_2005_9_16_2_87_0/

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